Relevant bibliographies by topics / Partial differential equations – Parabolic equations and systems – Heat equation

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Partial differential equations – Parabolic equations and systems – Heat equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Partial differential equations – Parabolic equations and systems – Heat equation.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Partial differential equations – Parabolic equations and systems – Heat equation"

1

Abdenova, Gaukhar, Karlygash Bazikova, and Zhangul Kenzhegalym. "A parabolic model in the form of space states of the dynamics of savings." Analysis and data processing systems, no. 2 (June 18, 2021): 7–18. http://dx.doi.org/10.17212/2782-2001-2021-2-7-18.

Full text
Abstract:
An important place in the theory of partial differential equations and its applications is occupied by the heat equation, a representative of the class of the so-called parabolic equations. It is known that to check the correctness of a mathematical model based on a parabolic equation, the existence of its solution is very important since a mathematical model is not always adequate to a specific phenomenon and the existence of a solution to a corresponding mathematical problem does not follow from the existence of a solution to a real applied problem. Therefore, methods for solving partial differential equations, both analytical and numerical, are always relevant. Nowadays, a computational experiment has become a powerful tool for theoretical research. It is carried out over a mathematical model of the object under study, but at the same time, other parameters are calculated using one of the parameters of the model and conclusions are drawn about the properties of the object or phenomenon under study. The problem of passive parametric identification of systems with distributed parameters for resource accumulation dynamics of many households using a stochastic distributed model in the form of a state space with regard to the white noise of the dynamics model of the object under study and the white noise of the model of a linear-type measuring system is considered in the paper. The use of the finite difference method allowed us to reduce the solution of partial differential equations of a parabolic type to the solution of a system of linear finite difference and algebraic equations represented by models in the form of a state space. It was also proposed to use a filtering algorithm based on the Kalman scheme for reliable estimation of the object behavior. Calculations were carried out using the Matlab mathematical system based on statistical data for five years, taken from the site “Agency for Strategic Planning and Reforms of the Republic of Kazakhstan Bureau of National Statistics”. Estimation of the coefficients of the equations for the household resource accumulation in the form of a state space using this technique is sufficiently universal and can be applied in other fields of science and technology.
APA, Harvard, Vancouver, ISO, and other styles
2

Friedly, J. C. "Transient Response of a Coupled Conduction and Convection Heat Transfer Problem." Journal of Heat Transfer 107, no. 1 (1985): 57–62. http://dx.doi.org/10.1115/1.3247402.

Full text
Abstract:
Systems of dynamic models involving the coupling of both conduction and convection offer significant theoretical challenges because of the interaction between parabolic and hyperbolic types of responses. Recent results of state space theory for coupled partial differential equation models are applied to conjugate heat transfer problems in an attempt to understand this interaction. Definition of a matrix of Green’s functions for such problems permits the transient responses to be resolved directly in terms of the operators’ spectral properties when they can be obtained. Application of the theory to a simple conjugate heat transfer problem is worked out in detail. The model consists of the transient energy storage or retrieval in a stationary, single dimensioned matrix through which an energy transport fluid flows. Even though the partial differential operator is nonself-adjoint, it is shown how its spectral properties can be obtained and used in the general solution. Computations are presented on the effect of parameters on the spectral properties and the nature of the solution. Comparison is made with several readily solvable limiting cases of the equations.
APA, Harvard, Vancouver, ISO, and other styles
3

Phan, Tuấn Đình, and Ha Ngoc Hoang. "NONLINEAR CONTROL OF TEMPERATURE PROFILE OF UNSTABLE HEAT CONDUCTION SYSTEMS: A PORT HAMILTONIAN APPROACH." Journal of Computer Science and Cybernetics 32, no. 1 (2016): 61–74. http://dx.doi.org/10.15625/1813-9663/32/1/6401.

Full text
Abstract:
This paper focuses on boundary control of distributed parameter systems (also called infinite dimensional systems). More precisely, a passivity based approach for the stabilization of temperature profile inside a well-insulated bar with heat conduction in a one-dimensional described by parabolic partial differential equations (PDEs) is developed. This approach is motivated by an appropriate model reduction schema using the finite difference approximation method. On this basis, it allows to discretize and then, write the original parabolic PDEs into a Port Hamiltonian (PH) representation. From this, the boundary control input is therefore synthesized using passive tools to stabilize the temperature at a desired reference profile asymptotically. The infinite dimensional nature of the original distributed parameter system in the PH framework is also discussed. Numerical simulations illustrate the application of the developments.
APA, Harvard, Vancouver, ISO, and other styles
4

Straughan, B. "Porous convection with local thermal non-equilibrium temperatures and with Cattaneo effects in the solid." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2157 (2013): 20130187. http://dx.doi.org/10.1098/rspa.2013.0187.

Full text
Abstract:
There is increasing interest in convection in local thermal non-equilibrium (LTNE) porous media. This is where the solid skeleton and the fluid may have different temperatures. There is also increasing interest in thermal wave motion, especially at the microscale and nanoscale, and particularly in solids. Much of this work has been based on the famous model proposed by Carlo Cattaneo in 1948. In this paper, we develop a model for thermal convection in a fluid-saturated Darcy porous medium allowing the solid and fluid parts to be at different temperatures. However, we base our thermodynamics for the fluid on Fourier's law of heat conduction, whereas we allow the solid skeleton to transfer heat by means of the Cattaneo heat flux theory. This leads to a novel system of partial differential equations involving Darcy's law, a parabolic fluid temperature equation and effectively a hyperbolic solid skeleton temperature equation. This system leads to novel physics, and oscillatory convection is found, whereas for the standard LTNE Darcy model, this does not exist. We are also able to derive a rigorous nonlinear global stability theory, unlike work in thermal convection in other second sound systems in porous media.
APA, Harvard, Vancouver, ISO, and other styles
5

Eremin, A. V., and K. V. Gubareva. "Analytical solution to the problem of heat transfer using boundary conditions of the third kind." Vestnik IGEU, no. 6 (2019): 67–74. http://dx.doi.org/10.17588/2072-2672.2019.6.067-074.

Full text
Abstract:
Non-stationary heat transmission within solid bodies is described using parabolic and hyperbolic equations. Currently, numerical methods for studying the processes of heat and mass transfer in the flows of liquids and gases have disseminated. Modern programs allow the automatic construction of computational grids, solutions to the systems of equations and offer a wide range of tools for analysis. Approximate analytical solutions have significant advantages compared to numerical ones. In particular, the solutions obtained in an analytical form allow performing parametric analysis of the system under study, configuration and programming of measurement devices, etc. Based on the joint use of additional desired function and additional boundary conditions in the integral method of heat balance, a method of mathematical modeling for the heat transfer process in a plate under symmetric boundary conditions of the third kind has been developed. Using the heat flux density as a new desired function, the method for solving heat conduction problems with boundary conditions of the third kind has been proposed. Finding a solution to the partial differential equation with respect to the temperature function presents integrating an ordinary differential equation with respect to the heat flux density on the surface of the studied zone. It has been shown that isotherms appear on the surface of the plate with a certain initial velocity which depends on the heat transfer intensity. The calculation results have been compared to the exact solution. The presented method can be used in determining the heat flux density of buildings and heating devices, finding heat losses during convective heat transfer and designing heat transfer equipment. The results can be applied to increase the validity and reliability of the calculation of actual losses and balance of thermal energy. The method reliability, validity and a high degree of approximation with about 3% inaccuracy have been demonstrated. The accuracy of the solution depends on the number of approximations performed and is determined by the degree of the approximating polynomial.
APA, Harvard, Vancouver, ISO, and other styles
6

Cruz-Quintero, Eduardo, and Francisco Jurado. "Boundary Control for a Certain Class of Reaction-Advection-Diffusion System." Mathematics 8, no. 11 (2020): 1854. http://dx.doi.org/10.3390/math8111854.

Full text
Abstract:
There are physical phenomena, involving diffusion and structural vibrations, modeled by partial differential equations (PDEs) whose solution reflects their spatial distribution. Systems whose dynamics evolve on an infinite-dimensional Hilbert space, i.e., infinite-dimensional systems, are modeled by PDEs. The aim when designing a controller for infinite-dimensional systems is similar to that for finite-dimensional systems, i.e., the control system must be stable. Another common goal is to design the controller in such a way that the response of the system does not be affected by external disturbances. The controller design for finite-dimensional systems is not an easy task, so, the controller design for infinite-dimensional systems is even more challenging. The backstepping control approach is a dominant methodology for boundary feedback design. In this work, we try with the backstepping design for the boundary control of a reaction-advection-diffusion (R-A-D) equation, namely, a type parabolic PDE, but with constant coefficients and Neumann boundary conditions, with actuation in one of these latter. The heat equation with Neumann boundary conditions is considered as the target system. Dynamics of the open- and closed-loop solution of the PDE system are validated via numerical simulation. The MATLAB®-based numerical algorithm related with the implementation of the control scheme is here included.
APA, Harvard, Vancouver, ISO, and other styles
7

JOSHI, DHRUTI B., and A. K. DESAI. "Reduction of Certain Type of Parabolic Partial Differential Equations to Heat Equation." Journal of Ultra Scientist of Physical Sciences Section A 30, no. 9 (2018): 353–61. http://dx.doi.org/10.22147/jusps-a/300901.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Jin, Sixian, and Henry Schellhorn. "Semigroup Solution of Path-Dependent Second-Order Parabolic Partial Differential Equations." International Journal of Stochastic Analysis 2017 (February 27, 2017): 1–12. http://dx.doi.org/10.1155/2017/2876961.

Full text
Abstract:
We apply a new series representation of martingales, developed by Malliavin calculus, to characterize the solution of the second-order path-dependent partial differential equations (PDEs) of parabolic type. For instance, we show that the generator of the semigroup characterizing the solution of the path-dependent heat equation is equal to one-half times the second-order Malliavin derivative evaluated along the frozen path.
APA, Harvard, Vancouver, ISO, and other styles
9

KUMAR, B. V. RATHISH, and MANI MEHRA. "A WAVELET-TAYLOR GALERKIN METHOD FOR PARABOLIC AND HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS." International Journal of Computational Methods 02, no. 01 (2005): 75–97. http://dx.doi.org/10.1142/s0219876205000375.

Full text
Abstract:
In this study a set of new space and time accurate numerical methods based on different time marching schemes such as Euler, leap-frog and Crank-Nicolson for partial differential equations of the form [Formula: see text], where ℒ is linear differential operator and [Formula: see text] is a nonlinear function, are proposed. To produce accurate temporal differencing, the method employs forward/backward time Taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation. This yields a generalized time discretized scheme which is approximated in space by Galerkin method. The compactly supported orthogonal wavelet bases developed by Daubechies are used in Galerkin scheme. This new wavelet-Taylor Galerkin approach is successively applied to heat equation, convection equation and inviscid Burgers' equation.
APA, Harvard, Vancouver, ISO, and other styles
10

Kafle, J., L. P. Bagale, and D. J. K. C. "Numerical Solution of Parabolic Partial Differential Equation by Using Finite Difference Method." Journal of Nepal Physical Society 6, no. 2 (2020): 57–65. http://dx.doi.org/10.3126/jnphyssoc.v6i2.34858.

Full text
Abstract:
In the real world, many physical problems like heat equation, wave equation, Laplace equation and Poisson equation are modeled by partial differential equations (PDEs). A PDE of the form ut = α uxx, (α > 0) where x and t are independent variables and u is a dependent variable; is a one-dimensional heat equation. This is an example of a prototypical parabolic equation. The heat equation has analytic solution in regular shape domain. If the domain has irregular shape, computing analytic solution of such equations is difficult. In this case, we can use numerical methods to compute the solution of such PDEs. Finite difference method is one of the numerical methods that is used to compute the solutions of PDEs by discretizing the given domain into finite number of regions. Here, we derived the Forward Time Central Space Scheme (FTCSS) for this heat equation. We also computed its numerical solution by using FTCSS. We compared the analytic solution and numerical solution for different homogeneous materials (for different values of diffusivity α). There is instantaneous heat transfer and heat loss for the materials with higher diffusivity (α) as compared to the materials of lower diffusivity. Finally, we compared simulation results of different non-homogeneous materials.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Partial differential equations – Parabolic equations and systems – Heat equation"

1

Le, Balc'h Kévin. "Contrôlabilité de systèmes de réaction-diffusion non linéaires." Thesis, Rennes, École normale supérieure, 2019. http://www.theses.fr/2019ENSR0016/document.

Full text
Abstract:
Cette thèse est consacrée au contrôle de quelques équations aux dérivées partielles non linéaires. On s’intéresse notamment à des systèmes paraboliques de réaction-diffusion non linéaires issus de la cinétique chimique. L’objectif principal est de démontrer des résultats de contrôlabilité locale ou globale, en temps petit, ou en temps grand.Dans une première partie, on démontre un résultat de contrôlabilité locale à des états stationnaires positifs en temps petit, pour un système de réaction-diffusion non linéaire.Dans une deuxième partie, on résout une question de contrôlabilité globale à zéro en temps petit pour un système 2 × 2 de réaction-diffusion non linéaire avec un couplage impair.La troisième partie est consacrée au célèbre problème ouvert d’Enrique Fernández-Cara et d’Enrique Zuazua des années 2000 concernant la contrôlabilité globale à zéro de l’équation de la chaleur faiblement non linéaire. On démontre un résultat de contrôlabilité globale à états positifs en temps petit et un résultat de contrôlabilité globale à zéro en temps long.La dernière partie, rédigée en collaboration avec Karine Beauchard et Armand Koenig, est une incursion vers l’hyperbolique. On étudie des systèmes linéaires à coefficients constants, couplant une dynamique transport avec une dynamique parabolique. On identifie leur temps minimal de contrôle et l’influence de leur structure algébrique sur leurs propriétés de contrôle<br>This thesis is devoted to the control of nonlinear partial differential equations. We are mostly interested in nonlinear parabolic reaction-diffusion systems in reaction kinetics. Our main goal is to prove local or global controllability results in small time or in large time.In a first part, we prove a local controllability result to nonnegative stationary states in small time, for a nonlinear reaction-diffusion system.In a second part, we solve a question concerning the global null-controllability in small time for a 2 × 2 nonlinear reaction-diffusion system with an odd coupling term.The third part focuses on the famous open problem due to Enrique Fernndez-Cara and Enrique Zuazua in 2000, concerning the global null-controllability of the weak semi-linear heat equation. We show that the equation is globally nonnegative controllable in small time and globally null-controllable in large time.The last part, which is a joint work with Karine Beauchard and Armand Koenig, enters the hyperbolic world. We study linear parabolic-transport systems with constant coeffcients. We identify their minimal time of control and the influence of their algebraic structure on the controllability properties
APA, Harvard, Vancouver, ISO, and other styles
2

Comte, Eloïse. "Pollution agricole des ressources en eau : approches couplées hydrogéologique et économique." Thesis, La Rochelle, 2017. http://www.theses.fr/2017LAROS029/document.

Full text
Abstract:
Ce travail s’inscrit dans un contexte de contrôle de la pollution des ressources en eau. On s’intéresse plus particulièrement à l’impact des engrais d’origine agricole sur la qualité de l’eau, en alliant modélisation économique et hydrogéologique. Pour cela, nous définissons d’une part un objectif économique spatio-temporel prenant en compte le compromis entre l’utilisation d’engrais et les coûts de dépollution. D’autre part, nous décrivons le transport du polluant dans le sous-sol (3D en espace) par un système non linéaire d’équations aux dérivées partielles couplées de type parabolique (réaction-convection-dispersion) et elliptique dans un domaine borné. Nous prouvons l’existence globale d’une solution au problème de contrôle optimal. L’unicité est quant à elle démontrée par analyse asymptotique pour le problème effectif tenant compte de la faible concentration d’engrais en sous-sol. Nous établissons les conditions nécessaires d’optimalité et le problème adjoint associé à notre modèle. Quelques exemples analytiques sont donnés et illustrés. Nous élargissons ces résultats au cadre de la théorie des jeux, où plusieurs joueurs interviennent, et prouvons notamment l’existence d’un équilibre de Nash. Enfin, ce travail est illustré par des résultats numériques (2D en espace), obtenus en couplant un schéma de type Éléments Finis Mixtes avec un algorithme de gradient conjugué non linéaire<br>This work is devoted to water ressources pollution control. We especially focus on the impact of agricultural fertilizer on water quality, by combining economical and hydrogeological modeling. We define, on one hand, the spatio-temporal objective, taking into account the trade off between fertilizer use and the cleaning costs. On an other hand, we describe the pollutant transport in the underground (3D in space) by a nonlinear system coupling a parabolic partial differential equation (reaction-advection-dispersion) with an elliptic one in a bounded domain. We prove the global existence of the solution of the optimal control problem. The uniqueness is proved by asymptotic analysis for the effective problem taking into account the low concentration fertilizer. We define the optimal necessary conditions and the adjoint problem associated to the model. Some analytical results are provided and illustrated. We extend these results within the framework of game theory, where several players are involved, and we prove the existence of a Nash equilibrium. Finally, this work is illustrated by numerical results (2D in space), produced by coupling a Mixed Finite Element scheme with a nonlinear conjugate gradient algorithm
APA, Harvard, Vancouver, ISO, and other styles
3

Li, Xiaodong. "Observation et commande de quelques systèmes à paramètres distribués." Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00456850.

Full text
Abstract:
L'objectif principal de cette thèse consiste à étudier plusieurs thématiques : l'étude de l'observation et la commande d'un système de structure flexible et l'étude de la stabilité asymptotique d'un système d'échangeurs thermiques. Ce travail s'inscrit dans le domaine du contrôle des systèmes décrits par des équations aux dérivées partielles (EDP). On s'intéresse au système du corps-poutre en rotation dont la dynamique est physiquement non mesurable. On présente un observateur du type Luenberger de dimension infinie exponentiellement convergent afin d'estimer les variables d'état. L'observateur est valable pour une vitesse angulaire en temps variant autour d'une constante. La vitesse de convergence de l'observateur peut être accélérée en tenant compte d'une seconde étape de conception. La contribution principale de ce travail consiste à construire un simulateur fiable basé sur la méthode des éléments finis. Une étude numérique est effectuée pour le système avec la vitesse angulaire constante ou variante en fonction du temps. L'influence du choix de gain est examinée sur la vitesse de convergence de l'observateur. La robustesse de l'observateur est testée face à la mesure corrompue par du bruit. En mettant en cascade notre observateur et une loi de commande stabilisante par retour d'état, on souhaite obtenir une stabilisation globale du système. Des résultats numériques pertinents permettent de conjecturer la stabilité asymptotique du système en boucle fermée. Dans la seconde partie, l'étude est effectuée sur la stabilité exponentielle des systèmes d'échangeurs thermiques avec diffusion et sans diffusion. On établit la stabilité exponentielle du modèle avec diffusion dans un espace de Banach. Le taux de décroissance optimal du système est calculé pour le modèle avec diffusion. On prouve la stabilité exponentielle dans l'espace Lp pour le modèle sans diffusion. Le taux de décroissance n'est pas encore explicité dans ce dernier cas.
APA, Harvard, Vancouver, ISO, and other styles
4

Fernandez, Tasha N. "Analytical Computation of Proper Orthogonal Decomposition Modes and n-Width Approximations for the Heat Equation with Boundary Control." 2010. http://trace.tennessee.edu/utk_gradthes/794.

Full text
Abstract:
Model reduction is a powerful and ubiquitous tool used to reduce the complexity of a dynamical system while preserving the input-output behavior. It has been applied throughout many different disciplines, including controls, fluid and structural dynamics. Model reduction via proper orthogonal decomposition (POD) is utilized for of control of partial differential equations. In this thesis, the analytical expressions of POD modes are derived for the heat equation. The autocorrelation function of the latter is viewed as the kernel of a self adjoint compact operator, and the POD modes and corresponding eigenvalues are computed by solving homogeneous integral equations of the second kind. The computed POD modes are compared to the modes obtained from snapshots for both the one-dimensional and two-dimensional heat equation. Boundary feedback control is obtained through reduced-order POD models of the heat equation and the effectiveness of reduced-order control is compared to the full-order control. Moreover, the explicit computation of the POD modes and eigenvalues are shown to allow the computation of different n-widths approximations for the heat equation, including the linear, Kolmogorov, Gelfand, and Bernstein n-widths.
APA, Harvard, Vancouver, ISO, and other styles
5

Gaudiano, Marcos Enrique. "Problemas de frontera libre en la difusión de solventes de polímeros /." Doctoral thesis, 2008. http://hdl.handle.net/11086/116.

Full text
Abstract:
Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física, 2008.<br>El estudio de la difusión de solventes en polímeros es de gran utilidad en la industria de los materiales plásticos. Matemáticamente, estos procesos pueden ser modelados como problemas de frontera libre.<br>Research in diffusion of solvent into polymers is an important challenge which arises in polymer industry. Mathematically, these processes can be modelled as free boundary problems. We studied the one dimensional case. Imposing a convective boundary condition on the fixed face, the solution has an interesting asymptotic behavior. It is found that the free boundary is bounded by a constant which does not depend on the conductivity coefficient, which holds even if the diffusion process is nonlinear. Numerical methods are presented to compute the solutions and compare the results.<br>Marcos Enrique Gaudiano ; Cristina V. Turner.
APA, Harvard, Vancouver, ISO, and other styles

Books on the topic "Partial differential equations – Parabolic equations and systems – Heat equation"

1

Random walk and the heat equation. American Mathematical Society, 2010.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Introduction to heat potential theory. American Mathematical Society, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

Watson, N. A. Introduction to heat potential theory. American Mathematical Society, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Lectures on linear partial differential equations. American Mathematical Society, 2011.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Fokker-Planck-Kolmogorov equations. American Mathematical Society, 2015.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

Habib, Ammari, Capdeboscq Yves 1971-, and Kang Hyeonbae, eds. Multi-scale and high-contrast PDE: From modelling, to mathematical analysis, to inversion : Conference on Multi-scale and High-contrast PDE:from Modelling, to Mathematical Analysis, to Inversion, June 28-July 1, 2011, University of Oxford, United Kingdom. American Mathematical Society, 2010.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Steven, Rosenberg, and Clara L. Aldana. Analysis, geometry, and quantum field theory: International conference in honor of Steve Rosenberg's 60th birthday, September 26-30, 2011, Potsdam University, Potsdam, Germany. American Mathematical Society, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Partial differential equations – Parabolic equations and systems – Heat equation"

1

Jost, Jürgen. "Existence Techniques II: Parabolic Methods. The Heat Equation." In Partial Differential Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4809-9_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Ebert, Marcelo R., and Michael Reissig. "Heat Equation—Properties of Solutions—Starting Point of Parabolic Theory." In Methods for Partial Differential Equations. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-66456-9_9.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

"Existence Techniques II: Parabolic Methods. The Heat Equation." In Partial Differential Equations. Springer New York, 2007. http://dx.doi.org/10.1007/978-0-387-49319-0_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

"Solving Two-Dimensional Partial Differential Equations." In Advances in Systems Analysis, Software Engineering, and High Performance Computing. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-7078-4.ch008.

Full text
Abstract:
This chapter describes the PDE Modeler tool, which is used to solve spatially two-dimensional partial differential equations (PDE). It begins with a description of the standard forms of PDEs and its initial and boundary conditions that the tool uses. It is shown how various PDEs and boundary conditions can be represented in standard forms. Applications to the mechanics and tribology are presented in the final part of the chapter. They illustrate the use of PDE Modeler to solve the Reynolds equation describing the hydrodynamic lubrication, to implement the mechanical stress modeler application for a plate with an elliptical hole, to solve the transient heat equation with temperature-dependent material properties, and to study vibration of a rectangular membrane.
APA, Harvard, Vancouver, ISO, and other styles
5

Lorenzi, Luca, and Abdelaziz Rhandi. "Prelude to Parabolic Equations: The Heat Equation and the Gauss-Weierstrass Semigroup in C b ( \mathbb R d )." In Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9780429262593-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Partial differential equations – Parabolic equations and systems – Heat equation"

1

Campo, Antonio, Ramin Soujoudi, and Adelina Davis. "The Transversal Method of Lines (TMOL) Applied to Unsteady Conduction in Large Plates, Long Cylinders and Spheres With Prescribed Surface Heat Flux." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-65279.

Full text
Abstract:
The Transversal Method Of Lines (TMOL) or Rothe method is a general technique for solving parabolic partial differential equations that uses a two-point backward finite-difference formulation for the time derivative and differential spatial derivatives. This hybrid approach leads to transformed ordinary differential equations where the spatial coordinate is the independent variable and the time appears as an embedded parameter. The transformed ordinary differential equations may have constant or variable coefficients depending on the coordinate system and are first-order accurate. In this work, TMOL is applied to the 1-D heat equation for large plates, long cylinders and spheres with constant thermophysical properties, uniform initial temperature and prescribed surface heat flux. The analytic solutions of the adjoint heat equations are performed with the symbolic Maple software. It is demonstrated that the approximate semi-analytic TMOL temperature distributions for the three simple bodies are much better than first-order accurate. This signifies that TMOL temperature distributions are not only valid for short times, but they are valid for the entire heating period involving short, moderate and long times.
APA, Harvard, Vancouver, ISO, and other styles
2

Karaki, Wafaa, Jon T. Van Lew, Peiwen Li, Cho Lik Chan, and Jake Stephens. "Heat Transfer in Thermocline Storage System With Filler Materials: Analytical Model." In ASME 2010 4th International Conference on Energy Sustainability. ASMEDC, 2010. http://dx.doi.org/10.1115/es2010-90209.

Full text
Abstract:
Parabolic trough power systems utilizing concentrated solar energy have proven their worth as a means for generating electricity. However, one major aspect preventing the technologies widespread acceptance is the deliverability of energy beyond a narrow window during peak hours of the sun. Thermal storage is a viable option to enhance the dispatchability of the solar energy and an economically feasible option is a thermocline storage system with a low-cost filler material. Utilization of thermocline storage facilities have been studied in the past and this paper hopes to expand upon that knowledge. The heat transfer between the heat transfer fluid and filler materials are governed by two conservation of energy equations, often referred as Schumann [1] equations. We solve these two coupled partial differential equations using Laplace transformation. The initial temperature distribution can be constant, linear or exponential. This flexibility allows us to apply the model to simulate unlimited charging and discharging cycles, similar to a day-to-day operation. The analytical model is used to investigate charging and discharging processes, and energy storage capacity. In an earlier paper [2], the authors presented numerical solution of the Schumann equations using method of characteristics. Comparison between analytical and numerical results shows that they are in very good agreement.
APA, Harvard, Vancouver, ISO, and other styles
3

Heydari, Ali, Bahar Firoozabadi, and Hamid Fazelli. "Mixed Convective Heat Transfer From Rotating Spheres." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/cie-6040.

Full text
Abstract:
Abstract This paper presents an analysis of flow and heat transfer over a rotating axsisymmetric body of revolution in a mixed convective heat transfer along with surface conditions of heating or cooling as well as surface transpriation. Boundary-layer approximation reduces the elliptic Navier-Stokes equations to parabolic equations, where the Keller-Cebeci method of finite-difference solution is used to solve the resulting system of partial-differential equations. Comparison of the calculated values of the velocity and temperature profiles as well as the shear and the heat transfer coefficients at the surface for the case of a sphere with the available literature data indicate the model well predicts the boundary-layer flow and heat transfer over a rotating axsisymmetric body.
APA, Harvard, Vancouver, ISO, and other styles
4

Waldron, Will. "A method for solving 2D nonlinear partial differential equations exemplified by the heat-diffusion equation." In Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXX, edited by Keith A. Krapels and Gerald C. Holst. SPIE, 2019. http://dx.doi.org/10.1117/12.2513623.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Venkataraman, P. "Explicit Solutions for Linear Partial Differential Equations Using Bezier Functions." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99227.

Full text
Abstract:
Solutions in basic polynomial form are obtained for linear partial differential equations through the use of Bezier functions. The procedure is a direct extension of a similar technique employed for nonlinear boundary value problems defined by systems of ordinary differential equations. The Bezier functions define Bezier surfaces that are generated using a bipolynomial Bernstein basis function. The solution is identified through a standard design optimization technique. The set up is direct and involves minimizing the error in the residuals of the differential equations over the domain. No domain discretization is necessary. The procedure is not problem dependent and is adaptive through the selection of the order of the Bezier functions. Three examples: (1) the Poisson equation; (2) the one dimensional heat equation; and (3) the slender two-dimensional cantilever beam are solved. The Bezier solutions compare excellently with the analytical solutions.
APA, Harvard, Vancouver, ISO, and other styles
6

Michopoulos, John G., Andrew Birnbaum, and Athanasios P. Iliopoulos. "Effect of Temperature Dependent Properties on the Applicability of the Heat Conduction Equations for Rapid Heat Deposition Applications." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59631.

Full text
Abstract:
Despite significant efforts examining the suitability of the proper form of the heat transfer partial differential equation (PDE) as a function of the time scale of interest (e.g. seconds, picoseconds, femtoseconds, etc.), very little work has been done to investigate the millisecond-microsecond regime. This paper examines the differences between the parabolic and one of the hyber-bolic forms of the heat conduction PDE that govern the thermal energy conservation on these intermediate timescales. Emphasis is given to the types of problems where relatively fast heat flux deposition is realized. Specifically, the classical parabolic form is contrasted against the lesser known Cattaneo-Vernotte hyperbolic form. A comparative study of the behavior of these forms over various pulsed conditions are applied at the center of a rectangular plate. Further emphasis is given to the variability of the solutions subject to constant or temperature-dependent thermal properties. Additionally, two materials, Al-6061 and refractory Nb1Zr, with widely varying thermal properties, were investigated.
APA, Harvard, Vancouver, ISO, and other styles
7

Elperin, Tov, Andrew Fominykh, and Zakhar Orenbakh. "Mass Transfer During Fluid Sphere Dissolution in an Alternating Electric Field." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56270.

Full text
Abstract:
In this study we considered mass transfer in a binary system comprising a stationary fluid dielectric sphere embedded into an immiscible dielectric liquid under the influence of an alternating electric field. Fluid sphere is assumed to be solvent-saturated so that an internal resistance to mass transfer can be neglected. Mass flux is directed from a fluid sphere to a host medium, and the applied electric field causes a creeping flow around the sphere. Droplet deformation under the influence of the electric field is neglected. The problem is solved in the approximations of a thin concentration boundary layer and finite dilution of a solute in the solvent. The thermodynamic parameters of a system are assumed constant. The nonlinear partial parabolic differential equation of convective diffusion is solved by means of a generalized similarity transformation, and the solution is obtained in a closed analytical form for all frequencies of the applied electric field. The rates of mass transfer are calculated for both directions of fluid motion — from the poles to equator and from the equator to the poles. Numerical calculations show essential (by a factor of 2–3) enhancement of the rate of mass transfer in water droplet–benzonitrile and droplet of carbontetrachloride–glycerol systems under the influence of electric field for a stagnant droplet. The asymptotics of the obtained solutions are discussed.
APA, Harvard, Vancouver, ISO, and other styles
8

Sensoy, Tugba S., Sam Yang, and Juan C. Ordonez. "Volume Element Model for Modeling, Simulation, and Optimization of Parabolic Trough Solar Collectors." In ASME 2017 11th International Conference on Energy Sustainability collocated with the ASME 2017 Power Conference Joint With ICOPE-17, the ASME 2017 15th International Conference on Fuel Cell Science, Engineering and Technology, and the ASME 2017 Nuclear Forum. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/es2017-3597.

Full text
Abstract:
In this paper we present a dynamic three-dimensional volume element model (VEM) of a parabolic trough solar collector (PTC) comprising an outer glass cover, annular space, absorber tube, and heat transfer fluid. The spatial domain in the VEM is discretized with lumped control volumes (i.e., volume elements) in cylindrical coordinates according to the predefined collector geometry; therefore, the spatial dependency of the model is taken into account without the need to solve partial differential equations. The proposed model combines principles of thermodynamics and heat transfer, along with empirical heat transfer correlations, to simplify the modeling and expedite the computations. The resulting system of ordinary differential equations is integrated in time, yielding temperature fields which can be visualized and assessed with scientific visualization tools. In addition to the mathematical formulation, we present the model validation using the experimental data provided in the literature, and conduct two simple case studies to investigate the collector performance as a function of annulus pressure for different gases as well as its dynamic behavior throughout a sunny day. The proposed model also exhibits computational advantages over conventional PTC models-the model has been written in Fortran with parallel computing capabilities. In summary, we elaborate the unique features of the proposed model coupled with enhanced computational characteristics, and demonstrate its suitability for future simulation and optimization of parabolic trough solar collectors.
APA, Harvard, Vancouver, ISO, and other styles
9

Bahmani, Bahador, and Amir R. Khoei. "Modeling Convective Heat Propagation in a Fractured Domain With X-FEM and Least Square Method." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-71167.

Full text
Abstract:
The main goal of the current study is developing an advanced and robust numerical tool for accurate capturing heat front propagation. In some applications such as impermeable medium, Heat transfer in the surrounding domain of fracture acts just as a conduction process but the heat transfer through the fractures appears as a convection process. From a mathematical point of view, a parabolic partial differential equation (PDE) should be solved in the surrounding domain whereas a hyperbolic PDE should be solved in the domain of fractures. In fact, they have completely different treatments and this is one of the complicated problems in this area. In this paper, the presence of fractures and discontinuities are considered with the aim of eXtended Finite Element Method (X-FEM). In the proposed numerical approach, the domain is decomposed into local and global scales. Global and local domains are solved by the X-FEM and Least Square Method (LSM) techniques, respectively. As a final result, it is determined that the treatment of coupling term between two scales is one of the most important factors for system performance. Increasing its effect can significantly improve the efficiency of the whole system.
APA, Harvard, Vancouver, ISO, and other styles
10

Joyot, Pierre, Nicolas Verdon, Gaël Bonithon, Francisco Chinesta, and Pierre Villon. "PGD-BEM Applied to the Nonlinear Heat Equation." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82407.

Full text
Abstract:
The Boundary Element Method (BEM) allows efficient solution of partial differential equations whose kernel functions are known. The heat equation is one of these candidates when the thermal parameters are assumed constant (linear model). When the model involves large physical domains and time simulation intervals the amount of information that must be stored increases significantly. This drawback can be circumvented by using advanced strategies, as for example the multi-poles technique. We propose radically different approach that leads to a separated solution of the space and time problems within a non-incremental integration strategy. The technique is based on the use of a space-time separated representation of the unknown field that, introduced in the residual weighting formulation, allows to define a separated solution of the resulting weak form. The spatial step can be then treated by invoking the standard BEM for solving the resulting steady state problem defined in the physical space. Then, the time problem that results in an ordinary first order differential equation is solved using any standard appropriate integration technique (e.g. backward finite differences). When considering the nonlinear heat equation, the BEM cannot be easily applied because its Green’s kernel is generally not known but the use of the PGD presents the advantage of rewriting the problem in such a way that the kernel is now clearly known. Indeed, the system obtained by the PGD is composed of a Poisson equation in space coupled with an ODE in time so that the use of the BEM for solving the spatial part of the problem is efficient. During the solving, we must however separate the nonlinear term into a space-time representation that can limit the method in terms of CPU time and storage, that is why we introduce in the second part of the paper a new approach combining the PGD and the Asymptotic Numerical Method (ANM) in order to efficiently treat the nonlinearity.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Partial differential equations – Parabolic equations and systems – Heat equation' for particular source types:
Journal articles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography